My posts

Solving Laplace’s Equation using Separation of Variables

Differential-Equation

Learn how to solve stationary heat distribution problem under specific boundary conditions

Basics of Projective Space and Projective Linear Group 射影空间与射影线性群

Algebra

Differential-Geometry

Projective spaces, unit quaternions, \(SU(2), SO(3)\), 3-sphere, Möbius transformations, double cover, etc.

UAV Control 无人机控制原理

Control-Theory

基于四元数的无人机姿态控制原理 (待完成)

PDE: Wave and Heat Equations Made Obvious 推导波动方程与热传导方程

Differential-Equation

First chapter of PDE series!

Understanding Isomorphism Theorems for Groups 群同构定理的理解

Algebra

If you struggle to have a clear mental picture of the isomorphism theorems, I hope this helps.

Control Case Study: LQR for Inverted Pendulum!

Control-Theory

Complete guide for building a linear feedback control system for an inverted pendulum in MATLAB.

Special Matrices 特殊矩阵与算子

Algebra

正规矩阵、厄米矩阵、酉矩阵、反厄米矩阵等性质

Three ways to Understand the Mixed Product of Vectors! 向量混合积的三种理解

Differential-Geometry

When it comes to \(a \cdot (b \times c)\), what’s in your head?

EM Chapter I: Maxwell’s First Equation

Physics

Understand \(\mathbf{\nabla} \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}\) in one article!

Q&A: Basis vectors are exactly the same as partial derivative operator? 为什么向量等价于微分算子?

Differential-Geometry

Why \(e_i\) is exactly the same as \(\frac{\partial}{\partial x^i}\)? How to define tangent space at some point of a manifold?

What is symmetry? 什么是对称性?

Algebra

Symmetry is nothing but a group acts on an object!

JK Flip-flop not Behavioral (VHDL version)

Hardware

Easy to write a behavioral description of JK-FF in VHDL, what about writing it in terms of gates?

在 ios 下载第三方应用

Awesome-Mac

会闪退, 散了吧(´･_･`)

Least Squares as Projection 最小二乘法的投影解释

Algebra

Thinking least squares in this way really helps!

java项目导入Launchpad方案 MacOS

Awesome-Mac

我想在launchpad上面启动一个 java 项目，但是application只支持启动 .app 文件，怎么办？

Create your own website using Hugo on MacOS

CS

This is how I built my first personal website without any prior knowledge of HTML.

RTL Analysis on MacOS under 300MB

Awesome-Mac

Wanna compile verilog on MacOS but without programing an FPGA? Check this out!